An Algebraic Roadmap of Particle Theories

Abstract An optimal algebraic framework of particle physics has a number of checkpoints to pass. As a minimum, models should conform to the Coleman‐Mandula theorem (or establish a loophole), evade familiar fermion doubling problems, naturally explain the Standard Model's chirality, exclude B‐L gauge symmetry at low energy, and explain the existence of three generations. The framework introduced in ref. [1] is shown to passes checkpoints , and has yet to cross . The discussion is concluded by elucidating an unexpected appearance of spacetime symmetries.